Home page for the course

This page will change throughout the semester.

Note:  Previously given exams are available below in Postscript format, that can be printed with a Postscript printer.  The files can also be viewed and printed with Ghostscript and GSview.

The first exam:
This exam will be on Tuesday, February 11, and will be closed book.  You should find the exam fairly easy if you have studied the material collected in class and also the homework that was collected on Tuesday, February 4.  You should know how to do the following:

• Write down the augmented matrix for a system of equations.
• Put a system of equations (or its matrix) in reduced row-echelon form.
• Determine the rank of a matrix.
• Write down the solution set of s system of equations in terms of spanning vectors and a translation vector.
• Know about the dimension of the solution set of a system of equations, and whether the solution set represents a line, plane, etc.
• Know how to write down a system of linear equations in the form Ax = b, where A is the matrix for the system, x is the vector of unknowns, and b is the constant right-hand-side vector.

The second exam:

Postscript copy of the second exam
PDF copy of the second exam
Second exam answers, page 1
Second exam answers, page 2
 

The third exam:
The exam will be on Thursday, April 10, and will be closed book.  Besides looking over all of the homework and your notes from the class, be sure to review the following:

• How to write down a matrix for a linear transformation that maps the unit square into a given parallelogram.
• How to write down the matrix for a linear transformation that stretches one or more coordinate axes.
• How to write down the matrix for a linear transformation corresponding to a rotation in a plane spanned by two of the coordinate axes.
• How to interpret geometrically the product of two matrices.
• How to compute the LU factorization of a matrix.
• How to use the LU factorization of a matrix to solve a system of equations.

Answer to bonus problem

The final exam:
The exam will be on Tuesday, May 13 at 7:30AM, and will be closed book.  You will need to be able to do the following:

• Solve a system of equations by putting the system into reduced row echelon form.
• Solve a system of equations by producing, then using an LU factorization.
• Compute the eigenvalues and eigenvectors of a matrix by writing down the characteristic polynomial.
• Compute a basis for the null space of a matrix and write down a basis for the range.
• Compute the QR factorization of a matrix.